Dozens of the church's largest archdioceses, universities and other affiliated groups sued the Obama administration around the country this week, in one of the largest religious lawsuits in US history.

They argue that the US government is violating the religious freedom of bosses whose faith forbids them from using or approving of birth control.

Firms who do not comply with the law face large fines.

Cardinal Timothy Dolan of New York, the president of the US Conference of Catholic Bishops, accused Mr Obama of "strangling" the church with his health care policies.

"We have tried negotiation with the administration and legislation with the Congress, and we'll keep at it, but there's still no fix," said Cardinal Dolan. "Time is running out, and our valuable ministries and fundamental rights hang in the balance, so we have to resort to the courts now."

The battle threatens to badly damage Mr Obama's support in November's presidential election among Catholics, a group he won by 54 per cent to 45 over his Republican rival John McCain in 2008.

Under rules introduced as part of Mr Obama's overhaul of the US health care system last year, employers must offer contraceptive coverage as part of their employees' health insurance packages.

The rule, which was backed by research from the government's independent health advisers, was intended to improve the health of mothers and children by helping women to space out pregnancies.

While churches and other houses of worship were originally free to opt out of the mandate, it was still initially forced on religiously-affiliated charities, schools and other organisations.

Amid Catholic uproar earlier this year, Mr Obama announced a climbdown, allowing affiliated organisations to opt out as well. However, activists complain that the amendments are too restrictive.

To be exempt, groups must "propagate your Catholic faith in everything you do, you can serve only Catholics and employ only Catholics," Cardinal Dolan told CBS yesterday. "When did the government get in the business of defining for us the extent of our ministry?"

Church officials have claimed that Mother Teresa would not have qualified for the exemption because she cared for poor people without regard to whether or not they were Catholics.

Mr Obama's amendment also requires that insurance companies provide contraception where bosses will not, prompting complaints that firms will end up paying anyway via increased premiums.

Among the organisations suing the government is Notre Dame University, a large Catholic university in Indiana. Rev. John Jenkins, the university's president, said: "We do not seek to impose our religious beliefs on others – we simply ask that the government not impose its values on the university when those values conflict with our religious teachings."

The controversy is one of several surrounding "ObamaCare", Mr Obama's overhaul of the beleaguered American health care system. The US Supreme Court is due to rule next month on whether a measure forcing Americans to buy health insurance violates the US Constitution.